The course-level objectives for 6th grade math come from the Missouri Learning Standards. The competencies are divided by unit below; separate module-level objectives are located at the beginning of each assignment.

Ratios and Proportional Relationships (RP)

• Understand and use ratios to solve problems.
  • 6.RP.A.1 - Understand a ratio as a comparison of two quantities and represent these comparisons.
  • 6.RP.A.2 - Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate.
  • 6.RP.A.3 - Solve problems involving ratios and rates.
    • a. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane.
    • b. Solve unit rate problems.
    • c. Solve percent problems.
    • d. Convert measurement units within and between two systems of measurement.

Number Sense and Operations (NS)

• Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
  • 6.NS.A.1 - Compute and interpret quotients of positive fractions.
    • a. Solve problems involving division of fractions by fractions.
• Compute with non-negative multi-digit numbers, and find common factors and multiples.
  • 6.NS.B.2 - Demonstrate fluency with division of multi-digit whole numbers.
  • 6.NS.B.3 - Demonstrate fluency with addition, subtraction, multiplication and division of decimals.
  • 6.NS.B.4 - Find common factors and multiples.
    • a. Find the greatest common factor (GCF) and the least common multiple (LCM).
    • b. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers.
• Apply and extend previous understandings of numbers to the system of rational numbers.
  • 6.NS.C.5 - Use positive and negative numbers to represent quantities.
  • 6.NS.C.6 - Locate a rational number as a point on the number line.
    • a. Locate rational numbers on a horizontal or vertical number line.
    • b. Write, interpret, and explain problems of ordering of rational numbers.
    • c. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line.
  • 6.NS.C.7 - Understand that the absolute value of a rational number is its distance from 0 on the number line.
  • 6.NS.C.8 - Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3).

Expressions, Equations, and Inequalities (EEI)

• Apply and extend previous understandings of arithmetic to algebraic expressions.
  • 6.EEI.A.1 - Describe the difference between an expression and an equation.
  • 6.EEI.A.2 - Create and evaluate expressions involving variables and whole number exponents.
    • a. Identify parts of an expression using mathematical terminology.
    • b. Evaluate expressions at specific values of the variables.
    • c. Evaluate non-negative rational number expressions.
    • d. Write and evaluate algebraic expressions.
    • e. Understand the meaning of the variable in the context of the situation.
  • 6.EEI.A.3 - Identify and generate equivalent algebraic expressions using mathematical properties.
• Reason about and solve one-variable equations and inequalities.
  • 6.EEI.B.4 - Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true.
  • 6.EEI.B.5 - Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.
  • 6.EEI.B.6 - Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation.
  • 6.EEI.B.7 - Solve one-step linear equations in one variable involving non-negative rational numbers.
  • 6.EEI.B.8 - Recognize that inequalities may have infinitely many solutions.
    • a. Write an inequality of the form x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition.
    • b. Graph the solution set of an inequality.
• Represent and analyze quantitative relationships between dependent and independent variables.
  • 6.EEI.C.9 - Identify and describe relationships between two variables that change in relationship to one another.
    • a. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable.
    • b. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other.

Geometry and Measurement (GM)

• Solve problems involving area, surface area and volume.
  • 6.GM.A.1 - Find the area of polygons by composing or decomposing the shapes into rectangles or triangles.
  • 6.GM.A.2 - Find the volume of right rectangular prisms.
    • a. Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base.
    • b. Apply V = l * w * h and V = Bh to find the volume of right rectangular prisms.
  • 6.GM.A.3 - Solve problems by graphing points in all four quadrants of the Cartesian coordinate plane.
    • a. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane
    • b. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
    • c. Find distances between points with the same first coordinate or the same second coordinate.
    • d. Construct polygons in the Cartesian coordinate plane.
  • 6.GM.A.4 - Solve problems using nets.
    • a. Represent three-dimensional figures using nets made up of rectangles and triangles.
    • b. Use nets to find the surface area of three-dimensional figures whose sides are made up of rectangles and triangles.

Data Analysis, Statistics, and Probability (DSP)

• Develop understanding of statistical variability.
  • 6.DSP.A.1 - Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
  • 6.DSP.A.2 - Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape.
  • 6.DSP.A.3 - Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number.
• Summarize and describe distributions.
  • 6.DSP.B.4 - Display and interpret data.
    • a. Use dot plots, histograms and box plots to display and interpret numerical data.
    • b. Create and interpret circle graphs.
  • 6.DSP.B.5 - Summarize numerical data sets in relation to the context.
    • a. Report the number of observations.
    • b. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement.
    • c. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data.
    • d. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data.